On kernel design for regularized LTI system identification

Chen, Tianshi

doi:10.1016/j.automatica.2017.12.039

Cited by 103 publications

(53 citation statements)

References 40 publications

(143 reference statements)

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“…In these methods, the system identification problem is formulated as a regularized regression problem where a regularization term is considered for penalizing the feasible solutions which do not match the prior knowledge. This prior knowledge can include the stability of the system, the smoothness of the impulse response, time constants and resonant frequencies [14]. According to the realization theory of positive systems [6], a transfer function of an external positive system has an internal positive realization if the transfer function has a special structured form.…”

Section: Introductionmentioning

confidence: 99%

Kernel-Based Identification of Positive Systems

Khosravi

Smith

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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In this paper, we introduce a novel method for identification of internally positive systems. In this regard, we consider a kernel-based regularization framework. For the existence of a positive realization of a given transfer function, necessary and sufficient conditions are introduced in the realization theory of the positive systems. Utilizing these conditions, we formulate a convex optimization problem by which we can derive a positive system for a given set of inputoutput data. The optimization problem is initially introduced in reproducing kernel Hilbert spaces where stable kernels are used for estimating the impulse response of system. Following that, employing theory of optimization in function spaces as well as the well-known representer theorem, an equivalent convex optimization problem is derived in finite dimensional Euclidean spaces which makes it suitable for numerical simulation and practical implementation. Finally, we have numerically verified the method by means of an example and a Monte Carlo analysis.

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Section: Introductionmentioning

confidence: 99%

Kernel-Based Identification of Positive Systems

Khosravi

Smith

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…In practice, we need to develop systematic ways to design kernels to embed various types of prior knowledge. Interestingly, Chen (2018), finds that the SS and DC kernels share some common properties and has developed, based on this finding, two systematic ways of kernel design methods: one is from a machine learning perspective and the other one is from a system theory perspective.…”

Section: Kernel Structurementioning

confidence: 99%

A shift in paradigm for system identification

Ljung

Chen

2019

International Journal of Control

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110

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System identification is a mature research area with well established paradigms, mostly based on classical statistical methods. Recently, there has been considerable interest in so called kernel-based regularisation methods applied to system identification problem. The recent literature on this is extensive and at times difficult to digest. The purpose of this contribution is to provide an accessible account of the main ideas and results of kernel-based regularisation methods for system identification. The focus is to assess the impact of these new techniques on the field and traditional paradigms.

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“…For the first order kernel, prior information about smoothness and exponential decay of the impulse response can be imposed by the so-called Diagonal/Correlated (DC) [2], [1], [11] structure of P 1 :…”

Section: Regularization For the First Order Volterra Kernelmentioning

confidence: 99%

Regularized nonparametric Volterra kernel estimation

et al. 2017

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In this paper, the regularization approach introduced recently for nonparametric estimation of linear systems is extended to the estimation of nonlinear systems modelled as Volterra series. The kernels of order higher than one, representing higher dimensional impulse responses in the series, are considered to be realizations of multidimensional Gaussian processes. Based on this, prior information about the structure of the Volterra kernel is introduced via an appropriate penalization term in the least squares cost function. It is shown that the proposed method is able to deliver accurate estimates of the Volterra kernels even in the case of a small amount of data points.

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On kernel design for regularized LTI system identification

Cited by 103 publications

References 40 publications

Kernel-Based Identification of Positive Systems

Kernel-Based Identification of Positive Systems

A shift in paradigm for system identification

Regularized nonparametric Volterra kernel estimation

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